+0

# help

+1
99
5

If a and b are integers such that a - b = 100, find the minimum value of a*b.

Jun 13, 2020

#1
+2

"deleted" realized my answer is wrong

Jun 13, 2020
edited by amazingxin777  Jun 13, 2020
edited by amazingxin777  Jun 13, 2020
edited by amazingxin777  Jun 13, 2020
#2
+1

if negatives are fine, then its -2500

if it's only positive answers, then I'm pretty sure its 101

Jun 13, 2020
edited by lokiisnotdead  Jun 13, 2020
edited by lokiisnotdead  Jun 13, 2020
#3
+2

the minimum value of b = 1 so the minimum value of a = 101      1*101= 101

Jun 13, 2020
#4
+1

The closer two numbers with the same sum are, the bigger their product.

In this case, the problem did not specify whether positive or negative so the minimum value is: 50-(-50)=100

Therefore, a*b= -2500

Jun 13, 2020
#5
0

Because $$(a,b )\in \mathbb Z^2$$, it is optimal to minimize b and maximize a.

Because of that reason, if we choose (a, b) = (50, -50), then we get our minimum value, which is -2500.

(If a was larger, then b would be smaller. Same otherwise. It is actually optimal to choose |a| = |b|, or make |a| as close as |b|.)

Jun 13, 2020